Summary of the Data

## [1] "total # of years"
## [1] 6
## [1] "total # of sites"
## [1] 17
## [1] "total # of site - year combinations"
## [1] 34
## [1] "total # of quadrats"
## [1] 960

Table S1

Site KI2013 KI2014 KI2015a KI2015b KI2016b KI2017
VL2 20 0 0 0 0 26
VL1 0 0 28 0 30 0
VL5 30 0 0 0 0 19
L5 25 0 0 0 0 29
M10 28 0 0 0 0 29
L1 0 32 0 0 0 29
H2 30 0 0 0 0 30
VH3 29 0 0 0 30 0
VH1 0 0 30 0 0 29
VH2 0 0 0 30 0 30
L4 25 0 0 0 0 30
M3 0 0 0 30 0 29
M2 26 0 0 0 30 0
M1 0 0 0 30 0 29
M4 0 21 0 0 0 30
M6 28 0 0 0 30 0
VL3 0 0 0 29 30 0

Coverage Standardizing

Figure S2

Hill Diversity

85% Coverage

Figure S4

90% Coverage

Figure 2

Figure S5

95% Coverage

Figure S6

Modelling

Table 1 and S3

  • The following models were used to create Table 1 and S3

Hill-Richness - 85% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_85 %>% filter(Order.q == 0)
## 
##      AIC      BIC   logLik deviance df.resid 
##    145.9    159.6    -63.9    127.9       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 1.681    1.296   
##  Residual             1.345    1.160   
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 1.34 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                21.627418   8.951937   2.416  0.01569 *  
## poly(HD_Cont, 2)1           2.803237   3.003803   0.933  0.35070    
## poly(HD_Cont, 2)2          -7.392928   2.480773  -2.980  0.00288 ** 
## MHWAfter                   -3.386123   0.397763  -8.513  < 2e-16 ***
## NPP                        -0.010488   0.008529  -1.230  0.21880    
## poly(HD_Cont, 2)1:MHWAfter -3.881003   2.319335  -1.673  0.09426 .  
## poly(HD_Cont, 2)2:MHWAfter -5.319014   2.319335  -2.293  0.02183 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Shannon - 85% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_85 %>% filter(Order.q == 1)
## 
##      AIC      BIC   logLik deviance df.resid 
##    139.7    153.4    -60.8    121.7       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.6723   0.8199  
##  Residual             1.5317   1.2376  
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 1.53 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                18.874476   6.999493   2.697 0.007006 ** 
## poly(HD_Cont, 2)1           1.486186   2.494737   0.596 0.551357    
## poly(HD_Cont, 2)2          -7.202565   2.114405  -3.406 0.000658 ***
## MHWAfter                   -3.981801   0.424495  -9.380  < 2e-16 ***
## NPP                        -0.009140   0.006667  -1.371 0.170425    
## poly(HD_Cont, 2)1:MHWAfter -1.295889   2.475211  -0.524 0.600594    
## poly(HD_Cont, 2)2:MHWAfter -1.464260   2.475211  -0.592 0.554139    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Simpson - 85% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_85 %>% filter(Order.q == 2)
## 
##      AIC      BIC   logLik deviance df.resid 
##    134.1    147.8    -58.0    116.1       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.2205   0.4696  
##  Residual             1.5720   1.2538  
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 1.57 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                15.797135   5.856909   2.697 0.006993 ** 
## poly(HD_Cont, 2)1           0.431847   2.203590   0.196 0.844630    
## poly(HD_Cont, 2)2          -6.894496   1.904976  -3.619 0.000296 ***
## MHWAfter                   -4.149528   0.430046  -9.649  < 2e-16 ***
## NPP                        -0.007107   0.005578  -1.274 0.202606    
## poly(HD_Cont, 2)1:MHWAfter  0.006452   2.507578   0.003 0.997947    
## poly(HD_Cont, 2)2:MHWAfter  0.650767   2.507578   0.260 0.795234    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Richness - 90% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_90 %>% filter(Order.q == 0)
## 
##      AIC      BIC   logLik deviance df.resid 
##    160.6    174.3    -71.3    142.6       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 2.248    1.499   
##  Residual             2.236    1.495   
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 2.24 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                26.33526   10.70615   2.460  0.01390 *  
## poly(HD_Cont, 2)1           2.25169    3.63551   0.619  0.53568    
## poly(HD_Cont, 2)2          -7.56427    3.01898  -2.506  0.01223 *  
## MHWAfter                   -3.40016    0.51287  -6.630 3.36e-11 ***
## NPP                        -0.01337    0.01020  -1.310  0.19006    
## poly(HD_Cont, 2)1:MHWAfter -3.38301    2.99051  -1.131  0.25795    
## poly(HD_Cont, 2)2:MHWAfter -9.27442    2.99051  -3.101  0.00193 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Shannon - 90% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_90 %>% filter(Order.q == 1)
## 
##      AIC      BIC   logLik deviance df.resid 
##    142.2    155.9    -62.1    124.2       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.7734   0.8794  
##  Residual             1.6135   1.2702  
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 1.61 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                20.647140   7.336939   2.814 0.004891 ** 
## poly(HD_Cont, 2)1           1.309290   2.601744   0.503 0.614799    
## poly(HD_Cont, 2)2          -7.654438   2.200658  -3.478 0.000505 ***
## MHWAfter                   -4.310017   0.435690  -9.892  < 2e-16 ***
## NPP                        -0.009987   0.006989  -1.429 0.153020    
## poly(HD_Cont, 2)1:MHWAfter -1.134566   2.540487  -0.447 0.655168    
## poly(HD_Cont, 2)2:MHWAfter -2.188292   2.540487  -0.861 0.389036    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Simpson - 90% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_90 %>% filter(Order.q == 2)
## 
##      AIC      BIC   logLik deviance df.resid 
##    137.4    151.1    -59.7    119.4       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.1706   0.413   
##  Residual             1.7981   1.341   
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2):  1.8 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                16.355969   6.038214   2.709 0.006754 ** 
## poly(HD_Cont, 2)1           0.333748   2.299570   0.145 0.884604    
## poly(HD_Cont, 2)2          -7.333595   1.996033  -3.674 0.000239 ***
## MHWAfter                   -4.459612   0.459937  -9.696  < 2e-16 ***
## NPP                        -0.007108   0.005750  -1.236 0.216424    
## poly(HD_Cont, 2)1:MHWAfter  0.032907   2.681869   0.012 0.990210    
## poly(HD_Cont, 2)2:MHWAfter  0.710243   2.681869   0.265 0.791139    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Richness - 95% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_95 %>% filter(Order.q == 0)
## 
##      AIC      BIC   logLik deviance df.resid 
##    190.6    204.3    -86.3    172.6       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 1.099    1.049   
##  Residual             8.339    2.888   
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 8.34 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 33.23388   13.40053   2.480  0.01314 *  
## poly(HD_Cont, 2)1            0.09279    5.05260   0.018  0.98535    
## poly(HD_Cont, 2)2           -8.14172    4.37108  -1.863  0.06251 .  
## MHWAfter                    -3.72362    0.99046  -3.759  0.00017 ***
## NPP                         -0.01735    0.01276  -1.359  0.17405    
## poly(HD_Cont, 2)1:MHWAfter   0.98449    5.77534   0.170  0.86464    
## poly(HD_Cont, 2)2:MHWAfter -15.78242    5.77534  -2.733  0.00628 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Shannon - 95% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_95 %>% filter(Order.q == 1)
## 
##      AIC      BIC   logLik deviance df.resid 
##    146.3    160.0    -64.1    128.3       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.7406   0.8606  
##  Residual             1.9126   1.3830  
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 1.91 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                22.415702   7.603577   2.948 0.003198 ** 
## poly(HD_Cont, 2)1           1.149400   2.729324   0.421 0.673660    
## poly(HD_Cont, 2)2          -8.224279   2.319628  -3.546 0.000392 ***
## MHWAfter                   -4.722210   0.474357  -9.955  < 2e-16 ***
## NPP                        -0.010712   0.007243  -1.479 0.139113    
## poly(HD_Cont, 2)1:MHWAfter -0.619336   2.765955  -0.224 0.822824    
## poly(HD_Cont, 2)2:MHWAfter -3.092995   2.765955  -1.118 0.263466    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Simpson - 95% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + NPP + (1 | Site)
## Data: estimates_95 %>% filter(Order.q == 2)
## 
##      AIC      BIC   logLik deviance df.resid 
##    142.1    155.9    -62.1    124.1       25 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.07091  0.2663  
##  Residual             2.18515  1.4782  
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 2.19 
## 
## Conditional model:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                16.845214   6.298051   2.675  0.00748 ** 
## poly(HD_Cont, 2)1           0.281470   2.445658   0.115  0.90837    
## poly(HD_Cont, 2)2          -7.867812   2.136113  -3.683  0.00023 ***
## MHWAfter                   -4.788453   0.507027  -9.444  < 2e-16 ***
## NPP                        -0.007045   0.005997  -1.175  0.24012    
## poly(HD_Cont, 2)1:MHWAfter  0.163696   2.956453   0.055  0.95584    
## poly(HD_Cont, 2)2:MHWAfter  0.863167   2.956453   0.292  0.77032    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

NPP Sensitivity for 90% Coverage Models

Hill-Richness - 90% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + (1 | Site)
## Data: estimates_90 %>% filter(Order.q == 0)
## 
##      AIC      BIC   logLik deviance df.resid 
##    160.2    172.4    -72.1    144.2       26 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 2.588    1.609   
##  Residual             2.236    1.495   
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 2.24 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 12.3219     0.5327  23.132  < 2e-16 ***
## poly(HD_Cont, 2)1           -0.4501     3.1060  -0.145  0.88479    
## poly(HD_Cont, 2)2           -8.0667     3.1060  -2.597  0.00940 ** 
## MHWAfter                    -3.4002     0.5129  -6.630 3.36e-11 ***
## poly(HD_Cont, 2)1:MHWAfter  -3.3826     2.9905  -1.131  0.25800    
## poly(HD_Cont, 2)2:MHWAfter  -9.2746     2.9905  -3.101  0.00193 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Shannon - 90% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + (1 | Site)
## Data: estimates_90 %>% filter(Order.q == 1)
## 
##      AIC      BIC   logLik deviance df.resid 
##    142.1    154.3    -63.1    126.1       26 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.9632   0.9814  
##  Residual             1.6135   1.2702  
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2): 1.61 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 10.1768     0.3893  26.140  < 2e-16 ***
## poly(HD_Cont, 2)1           -0.7091     2.2701  -0.312 0.754748    
## poly(HD_Cont, 2)2           -8.0300     2.2701  -3.537 0.000404 ***
## MHWAfter                    -4.3100     0.4357  -9.892  < 2e-16 ***
## poly(HD_Cont, 2)1:MHWAfter  -1.1346     2.5405  -0.447 0.655171    
## poly(HD_Cont, 2)2:MHWAfter  -2.1883     2.5405  -0.861 0.389039    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hill-Simpson - 90% Coverage

##  Family: gaussian  ( identity )
## Formula:          qD ~ poly(HD_Cont, 2) * MHW + (1 | Site)
## Data: estimates_90 %>% filter(Order.q == 2)
## 
##      AIC      BIC   logLik deviance df.resid 
##    136.9    149.1    -60.4    120.9       26 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.2667   0.5165  
##  Residual             1.7981   1.3409  
## Number of obs: 34, groups:  Site, 17
## 
## Dispersion estimate for gaussian family (sigma^2):  1.8 
## 
## Conditional model:
##                            Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 8.90404    0.34851  25.549  < 2e-16 ***
## poly(HD_Cont, 2)1          -1.10294    2.03216  -0.543 0.587307    
## poly(HD_Cont, 2)2          -7.60083    2.03216  -3.740 0.000184 ***
## MHWAfter                   -4.45961    0.45994  -9.696  < 2e-16 ***
## poly(HD_Cont, 2)1:MHWAfter  0.03313    2.68187   0.012 0.990145    
## poly(HD_Cont, 2)2:MHWAfter  0.71020    2.68187   0.265 0.791151    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Average Losses

Table S4

## # A tibble: 1 × 2
##   HillRichness SEM_HillRichness
##          <dbl>            <dbl>
## 1         3.40            0.677
## # A tibble: 1 × 2
##   HillShannon SEM_HillShannon
##         <dbl>           <dbl>
## 1        4.31           0.461
## # A tibble: 1 × 2
##   HillSimpson SEM_HillSimpson
##         <dbl>           <dbl>
## 1        4.46           0.475
HD_Cat HillRichness SEM_HillRichness HillShannon SEM_HillShannon HillSimpson SEM_HillSimpson
Low 2.171669 2.0012430 4.718067 1.351232 5.398287 1.2872725
Medium 1.528426 0.9849155 3.599975 0.920359 4.247973 0.9774367
Very High 5.878684 0.8023107 5.008173 0.457817 4.396447 0.7869922
Very Low 4.650593 0.7913677 4.370886 1.061707 4.136228 1.0002427

Stressor Responses

Note: Notation in code is the same as the notation used in the manuscript equations. ## Figure 4 (a-c) ### (a) Richness

## 
##  supF test
## 
## data:  fs.AR_Richness
## sup.F = 11.747, p-value = 0.04207
## 
##   Optimal 2-segment partition: 
## 
## Call:
## breakpoints.Fstats(obj = fs.AR_Richness)
## 
## Breakpoints at observation number:
## 9 
## 
## Corresponding to breakdates:
## 0.4705882
## 
## Call:
## lm(formula = ARi ~ HD_Cont, data = subset(AR_Richness, HD_Cont <= 
##     34.82568))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33120 -0.09404 -0.05247  0.06128  0.40353 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.007277   0.120623   0.060    0.954
## HD_Cont     -0.008624   0.006049  -1.426    0.204
## 
## Residual standard error: 0.245 on 6 degrees of freedom
## Multiple R-squared:  0.253,  Adjusted R-squared:  0.1285 
## F-statistic: 2.032 on 1 and 6 DF,  p-value: 0.2039
## 
## Call:
## lm(formula = ARi ~ HD_Cont, data = subset(AR_Richness, HD_Cont >= 
##     34.82568))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41924 -0.08346  0.01550  0.11109  0.31368 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -0.645270   0.224780  -2.871   0.0240 *
## HD_Cont      0.011131   0.004173   2.667   0.0321 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2286 on 7 degrees of freedom
## Multiple R-squared:  0.5041, Adjusted R-squared:  0.4332 
## F-statistic: 7.115 on 1 and 7 DF,  p-value: 0.03212

(b) Shannon

## 
##  supF test
## 
## data:  fs.AR_Shannon
## sup.F = 4.1874, p-value = 0.6603
## 
##   Optimal 2-segment partition: 
## 
## Call:
## breakpoints.Fstats(obj = fs.AR_Shannon)
## 
## Breakpoints at observation number:
## 6 
## 
## Corresponding to breakdates:
## 0.2941176
## 
## Call:
## lm(formula = ARi ~ HD_Cont, data = AR_Shannon)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52141 -0.10142  0.01363  0.10337  0.41874 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0123912  0.0982697   0.126    0.901
## HD_Cont     0.0009721  0.0023673   0.411    0.687
## 
## Residual standard error: 0.2411 on 15 degrees of freedom
## Multiple R-squared:  0.01112,    Adjusted R-squared:  -0.05481 
## F-statistic: 0.1686 on 1 and 15 DF,  p-value: 0.6871

(c) Simpson

## 
##  supF test
## 
## data:  fs.AR_Simpson
## sup.F = 3.0115, p-value = 0.8588
## 
##   Optimal 2-segment partition: 
## 
## Call:
## breakpoints.Fstats(obj = fs.AR_Simpson)
## 
## Breakpoints at observation number:
## 6 
## 
## Corresponding to breakdates:
## 0.2941176
## 
## Call:
## lm(formula = ARi ~ HD_Cont, data = AR_Simpson)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.51342 -0.22950  0.06513  0.12951  0.46411 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  1.029e-01  1.165e-01   0.883    0.391
## HD_Cont     -3.229e-05  2.807e-03  -0.012    0.991
## 
## Residual standard error: 0.2859 on 15 degrees of freedom
## Multiple R-squared:  8.825e-06,  Adjusted R-squared:  -0.06666 
## F-statistic: 0.0001324 on 1 and 15 DF,  p-value: 0.991